\(\Leftrightarrow6\left(x-1\right)\left(x-2\right)+6x^2-x\left(x-1\right)=0\)
\(\Leftrightarrow6x^2-18x+12+6x^2-x^2+x=0\)
\(\Leftrightarrow11x^2-17x+12=0\)
\(\Delta=\left(-17\right)^2-4\cdot11\cdot12=-239< 0\)
Do đó: Phương trình vô nghiệm
\(\dfrac{x-2}{x}+\dfrac{x}{x-1}-\dfrac{11}{6}=0\)
\(\Leftrightarrow\) \(\dfrac{x^2-7x+12}{6x^2-6x}=0\)
\(\Leftrightarrow x^2-7x+12=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-4\right)=0\)
\(\Leftrightarrow\) \(\left[{}\begin{matrix}x-3=0\\x-4=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=4\end{matrix}\right.\)
\(\dfrac{x-2}{x}+\dfrac{x}{x-1}-\dfrac{11}{6}=0\)
=>\(\dfrac{x-2}{x}+\dfrac{x}{x-1}=\dfrac{11}{6}\)
=>\(\dfrac{6.\left(x-2\right).\left(x-1\right)}{x.6.\left(x-1\right)}+\dfrac{x.6}{x.6\left(x-1\right)}=\dfrac{11.x\left(x-1\right)}{6.x.\left(x-1\right)}\)
khử mẫu
=>6.(x-2).(x-1)+6x=11x.(x-1)
=>6.(x2-x-2x+2)+6x=11x2-11x
=>6x2-6x-12x+12+6x=11x2-11x
=>6x2-6x-12x+12+6x-11x2+11x=0
=>-5x2-x+12=0
=> pt vô nghiệm
